This invention relates generally to valuation methods and systems for the purpose of decision making, including pricing financial options and other derivatives and more particularly to methods and systems for predicting valuations utilizing more accurate techniques than that of the prior art.
Investment decisions largely determine the generation of wealth over time. However, people continually make investment decisions that turn out to be poor decisions. Investment decision rules can help users select an investment from among two or more investments such that the chosen investment will be the one with the highest net present value. The term investment decision rules may include terms “valuation”, “capital budgeting” and “investment-decision modeling”. The net present value of an investment is a current dollar estimate for the sum of all cash outflows and inflows throughout the investment's life, taking into account the time value of money.
Prior art methods of valuing an investment or decision do not generate reliable predictions and ignore many important factors that should be taken into account when valuing an investment or decision. For example, those who use predictive methods possess critically important knowledge about the degree of uncertainty that surrounds a future event. A user may know the approximate timeframe within which an event will take place, or a finite range of possible values for an event. Prior-art methods accept only one or two numbers, or offer a limited set of distributions, to describe the uncertainty surrounding a future event, so users must simplify knowledge to accommodate the input limitations of prior art methods. Any knowledge that the user has about uncertainty that cannot be expressed in one or two numbers, or by the limited set of distributions offered, is lost.
Prior art methods include: comparable transaction method; multiples method; ordinary payback period method; discounted payback period method; internal rate of return method; profitability index method; net present value methods; real options method; and Monte Carlo Simulation.
The comparable transaction method uses the recent sale price of a similar investment as a proxy price for an investment under consideration. The problem with this method is that it: ignores the timing of future cash flows; does not take investment risk into account; does not separate the risk of timing from the risk of magnitude; ignores the value created by opportunities to make changes to the investment through time as more information becomes available; is inaccurate if the recent sale price of the proxy investment is not representative of the investment under consideration; requires at least one recent sale of a comparable investment when there may have been none; and generates a single number for the valuation result when a probability distribution is more accurate.
The multiples method is widely used and simple to calculate. The multiples method multiplies an historical performance metric of an investment by a market-determined factor. Two examples of performance metrics used in the multiples method to value companies are: price/earnings ratio, and earnings before interest, tax, depreciation and amortization. The multiples method can lead to an incorrect investment decision because the method: ignores timing of future cash flows; ignores investment risk; ignores the value created by opportunities to make changes to the investment through time as more information becomes available; relies on market-determined factors which are arbitrarily assigned, usually across an industry, sector or other broad category, and may not be relevant to the investment under consideration; is sensitive to historical performance and accounting metrics which may have been manipulated, or may not represent future performance metrics; and generates a single number for the valuation result when a probability distribution is more accurate.
The payback period method is widely used and simple to calculate. This method is widely used and simple to calculate. The payback period method calculates the number of periods (usually measured in years) required for the sum of the project's expected cash flows to equal its initial cash outlay. According to the payback period method, a project is acceptable if its payback period is shorter than or equal to a specified numbers of periods. If the choice is between several mutually exclusive projects, the one with the shortest payback period should be selected. The payback period method favors projects that pay back quickly which is popular because early payback contributes to a firm's overall liquidity. The payback period method can lead to an incorrect investment decision because the method: ignores timing of future cash flows; ignores investment risk; ignores the value created by opportunities to make changes to the investment through time as more information becomes available; ignores expected cash flows beyond the cutoff period and as such is biased against long-term investments; and generates a single number for the valuation result when a probability distribution is more accurate.
The discounted payback period method, also known as economic payback period method, is less widely used and more difficult to calculate, the discounted payback period method calculates the number of periods, usually measured in years, required for the sum of the present values of the project's expected cash flows to equal its initial cash outlay. Unlike the payback period method, the discounted payback period method partly takes into account the time value of money and the project risk. The discounted payback period method, though, can lead to an incorrect investment decision because it: ignores the timing of future cash flows beyond the payback period; ignores investment risk beyond the payback period; does not separate the risk of timing from the risk of magnitude; ignores the value created by opportunities to make changes to the investment through time as more information becomes available; is biased against long-term investments; and generates a single number for the valuation result when a probability distribution is more accurate.
The internal rate of return method is widely used yet difficult to calculate, the internal rate of return method calculates a discount rate that makes the net percent value of the investment equal to zero. An investment should be accepted if its internal rate of return is higher that it's cost of capital (a minimum rate of return set by the investor) and should be rejected if it is lower. The internal rate of return method takes in account the time value of money. The risk of an investment does not enter into the computation of its internal rate of return. However, the internal rate of return method does consider the risk of the investment because the method compares the project's internal rate of return with the minimum rate of return. The comparison substitutes as a measure of investment risk. The internal rate of return method can lead to an incorrect investment decision because the method: can generate more than one internal rate of return or none at all if the sequence of future cash flows contains one or more negative cash flows; does not separate the risk of timing from the risk of magnitude; ignores the value created by opportunities to make changes to the investment through time as more information becomes available; and generates a single number for the valuation result when a probability distribution
The probability index method calculates the ratio of the present value of the investment's expected cash-flow stream to its initial cash outlay:
      Profitability    ⁢                  ⁢    index    =            Present      ⁢                          ⁢      value      ⁢                          ⁢              (                              CF            1                    ,                      CF            2                    ,          …          ⁢                                          ,                      CF            n                          )                    Initial      ⁢                          ⁢      cash      ⁢                          ⁢      outlay      
CF1, CF2, . . . CFn=cash flows generated by the investment
According to the profitability method, an investment should be accepted if its profitability index is greater than one and rejected if it is less than one. The Profitability index method takes into account both the time value of money and the risk of an investment because the project's cash flows are discounted at their cost of capital. The profitability index method can lead to an incorrect investment decision because the method does not differentiate between investments with different cash outlays because the rule provides relative not absolute measurements, does not separate the risk of timing from the risk of magnitude, ignores the value created by opportunities to make changes to the investment through time as more information becomes available and generates a single number for the valuation result when a probability distribution is more accurate.
The Net present value methods (also known as discounted cash flow methods) calculate a current-dollar estimate for the sum of all cash flows to and from an investment over the investments life, taking into account the time value of money. Net present value methods apply a discount rate to each future cash flow to take account of the time value of money. Variations of net present value methods include: economic profit method, adjusted present value method, and equity discounted cash flow method. Examples of software that embody net present value methods include: Excel, Matlab and Crystal Ball.
Net present value methods (DCF methods) measure value creation, adjust for the timing of expected cash flows, adjust for risk of expected cash flows and are additive. Net present value methods can lead to incorrect investment decisions because the methods: usually apply a single discount rate to all cash flows even though different discount rates should be applied to each cash flow depending on the risks of that cash flows; do not separate the risk of timing from the risk of magnitude; do not lend themselves to the use of multiple discount rate; overvalue near-term future cash flows and undervalue distant cash flows because the methods assume that uncertainty is directly proportional to time when uncertainty is proportional to the square root of time; assume that investment returns, when express as a percentage, are log-normally distributed, when in fact, they are not; are complex to apply to two or more projects of unequal size or unequal life spans; ignore the value created by opportunities to make changes to the investment through time as more information becomes available; and generate a single number for the valuation result when a probability distribution is more accurate.
Also known within the art is the use of equations. Mathematicians, physicists, engineers, and analysts who build computer programs to solve partial differential equation (“PDE”) modeling problems must be familiar not only with the mathematics and physics of their problems, but also with a variety of technological tools. Pragmatically, this problem-solving process involves thinking in terms of the tools, e.g., numerical software libraries, existing codes, and systems for connection software components. Decisions made using equations can suffer because, due to the complexity of the equations, more energy and effort is devoted to coding a solution than understanding the fundamentals of the problem.
Many problems in science, engineering, or finance can be modeled using partial differential equations. While many techniques are widely used for finding a solution for these PDE problems, producing accurate software code to generate a solution is difficult and time consuming. Programming such software code requires extensive domain knowledge of the problem, an understanding of the math, an understanding of advanced computer science techniques, and extensive testing and debugging. Therefore, other techniques are often used to model such problems.
Investment banks and derivative brokers make extensive use of sophisticated mathematical models to price the instruments, and once sold, to hedge the risk in their positions. The models used are basically of four types: analytical models, and three versions of approximate numerical models: Monte Carlo, lattices (binomial and trinomial trees) and finite differences. Monte Carlo simulation is a technique for estimating the solution of a numerical mathematical problem by means of an artificial sampling environment. This is an established numerical method for the valuation of derivatives securities. It major strength is flexibility, and it may be applied to almost any problem, including history-dependant claims or empirically characterized security processes.
Also known within the art are a host of simplifications, e.g., constant interest rates, constant volatility of the underlying assets, continuously paid dividends, etc, which allow analytic solutions to the Black-Scholes equation, the basic partial differential equation describing derivative securities. These analytic solutions are packaged in software libraries of “analytics”. Many packages exist. They may be used by traders for rough estimates, but all the assumptions required to make analytic solutions possible, usually render them too inaccurate for pricing complex derivative products. Major investment banks usually strip them out of any integrated software systems they may buy, and substitute their own numerical models.
Monte Carlo models calculate the value of an option by simulating thousands or millions of possible random paths the underlying assets prices may take, and averaging the option value over this set. Some early exercise features, i.e., American options, are unreliably priced, and the values of critical hedging parameters are often imprecise. Option parameters calculated in this way may converge to the correct answer slowly and are computationally expensive.
Monte Carlo simulation methods can lead to incorrect investment decisions because the methods: do not separate the risk of time from the risk of magnitude; do not lend themselves to use of multiple discount rates; allow the user only a limited set of distributions which do not match some future cash; assume that investment returns, when expressed as a percentage, are log-normally distributed, when in fact, they are not; are complex to apply to two or more projects of unequal size or unequal life spans; are complicated to understand; are tedious and time-consuming to apply correctly; and ignore the value created by opportunities to make changes to the investment through time as more information becomes available.
The real options method calculates a dollar value for management's opportunity to make changes to the investment through time as more information becomes available. The word “option” refers to management's choice to do, or not do, something in the future. The real options method is usually used in addition with the net present value method. Managers have many opportunities to enhance the value of an investment during its lifetime as circumstances change. Real options include: the option to expand, contract, delay or abandon a project at various stages of its like. Real options can be exercised to alter a project during its useful like. Options embedded in an investment are either worthless or have a positive value, so that net present value of an investment will always underestimate the value of an investment project unless it includes a value for real options. Real options are sometimes known as flexibility options. The value of an investment can and does change throughout the investment's life. For example, the cost of capital depends on information available at the time the investment is valid. The cost of capital takes into account many factors including: marketability of the product, selling price, risk of obsolescence, technology used in manufacturing, economic, regulatory, and tax environments. An investment that permits its management to adjust easily and at low cost to significant changes in these factors is more valuable than an investment that won't. The option to abandon a project is particularly valuable in the mining and oil extraction industries where the output (mineral or oil) prices are volatile. For example, the net present value of an oil reserve may be negative given the current market expectations regarding the future price of oil, however, because the development of the reserve can be postponed perhaps for many years, the capital expenditures needed to start the extraction of oil can be deferred until the market prices rise. And the more volatile the oil prices, the higher the chance that the net present value of the reserve will become positive and the higher the value of the option to defer the development of the reserve.
The real option method can lead to an incorrect investment decision because the method: requires information that may be difficult to obtain, unreliable or unavailable; requires information that, even if available and reliable, is usually misunderstood by those who are capable of using the method; is difficult to apply because it usually requires the adaptation or use of complex formulas and valuation concepts originally used to value options on financial instruments; due to the methods complexity, disqualifies valuable input from users who are knowledgeable yet innumerate; assumes that investment returns, when expressed as a percentage, are log-normally distributed, when they are not; is complex to apply to two or more projects of unequal size or unequal life spans; is complicated to understand; is tedious and time-consuming to apply; tends to overvalue investments because the method assumes that managers fully exercise options at the optimal time; does not separate the risk of timing from the risk of magnitude; and generates a single number for the valuation result when a probability distribution is more accurate.
As can be seen, there is a need within the art to provide methods and system which accounts for the specific risks of an investment, one that; separates the uncertainty of timing of a future cash flow with the uncertainty of magnitude of a future cash flow; assumes that uncertainty is proportional to the square root or time; is simple and easy to use and can provide a single number estimate for the for an investment or decision if required.